If the problem happens only with game discs, try temporarily removing your hard drive to see if that fixes the problem (see Add or remove an Xbox 360 Hard Drive). If your Xbox 360 console doesn't have a hard drive, skip to solution 6.

If this resolves the problem, reattach the hard drive and order a new Xbox 360 Hard Drive from Device Support (sign in with your Microsoft account). Console registration is required to replace a hard drive under warranty.